1. Field of the Invention
This invention relates to determining the frequencies and amplitudes of non-synchronous vibration in the blades on a rotating wheel such as a turbine wheel, and specifically, to making such determinations where the probes detecting blade position are not evenly spaced about the wheel.
2. Background Information
The present invention has particular application to the detection of non-synchronous vibrations in the blades on a turbine wheel in a steam generator, but it will be appreciated that it can be applied to vibration analysis in other rotating systems.
Turbine blades, because of their complex design, are subject to vibration at frequencies which correspond to natural frequencies of the blades. Each natural frequency is associated with a particular mode, each of which is a different combination of vibrational deflections such as along the rotational axis of the turbine, perpendicular to the rotational axis of the turbine, and so forth. To prevent excessive vibration of the blade about its normal position, prudent design practice dictates that the blades be constructed such that the frequencies of the lowest modes fall between harmonics of the operating frequency of the turbine. However, the blades may be excited by non-synchronous forces such as aerodynamic buffeting or flutter. This may occur even if the natural resonance frequencies of the blade are not near the harmonics of the running speed of the turbine. When the amplitude of the vibration exceeds a certain level, objectional stresses are set up in the blade. If the condition is not detected and remedied, the blade may eventually fracture resulting in an extremely costly forced outage of the machinery. Thus, a method and apparatus for detecting non-synchronous vibration is useful to prevent such damage.
It is known to use non-contacting proximity sensors or probes to detect blade vibration. The probes detect the actual time of arrival of each blade as it passes each probe. The difference between the actual time of arrival of each blade and its expected time of arrival, determined with the use of an additional probe which tracks rotation of the turbine wheel, produces a signal containing blade vibration information. Fourier analysis is applied to this signal to extract the blade vibration frequencies and amplitudes.
Testing for synchronous vibrations is conducted by the manufacturer using a large number of probes, such as sixteen, which, in accordance with the Nyquist Theorem, yields unambiguous resolution of synchronous frequencies up to the eighth harmonic. Such tests for synchronous vibrations are carried out in test cells under conditions where the 16 probes can be evenly spaced about the turbine wheel.
In order to detect non-synchronous blade vibrations, a two probe blade vibration measurement system (BVM) is typically used. Under the Nyquist Theorem, such a system can only uniquely identify frequencies up to the fundamental rotational frequency of the rotor, and vibrations at this fundamental rotational frequency and its harmonics are all folded down onto each other and can be ignored. However, the non-synchronous vibrations, which are invariably above the system fundamental frequency, fold down into the first harmonic where they can be measured. Since there are only a few modes of non-synchronous vibration of interest, which can be predicted, the two probe system has been employed to measure non-synchronous blade vibrations even when the non-synchronous vibration frequencies are greater than the first harmonic frequency.
While the synchronous vibration tests are conducted under conditions where the probes can be evenly spaced, such is not the case for the non-synchronous vibration testing or monitoring. Typically, the two probe system is applied to a turbine on-line to monitor for non-synchronous vibrations induced by operating conditions. Under such circumstances it is common to find obstructions in the installation which prevent even spacing of even the two probes. While it is commonly understood that even sampling is necessary when performing a fast Fourier transform, it has commonly not been recognized as being a problem when utilizing a full Fourier transform as is used in BVM systems.
However, I have discovered that, in fact, uneven sampling does distort the results achieved using Fourier analysis in BVM systems having unevenly spaced probes, and thus in particular, two probe systems which commonly have unevenly spaced probes.
There is a need therefore, for improved methods and systems for measuring non-synchronous vibrations in blades on rotating wheels such as turbine wheels employing unevenly spaced probes.
In particular, there is a need for such improvement in methods and systems utilizing two unevenly spaced probes such as those used to measure non-synchronous blade vibrations.